## INVESTIGATION 2
### MID-INTERVAL VALUES
When mid-interval values are used to represent all data values within each interval, what effect will this have on estimating the mean of the grouped data?
This table summarises the marks out of 50 received by students in a Physics examination. The exact results for each student have been lost.
Marks
Frequency
0 - 9
2
10 - 19
31
20 - 29
73
30 - 39
85
40 - 49
28
(1) Suppose that all of the students scored the lowest possible result in their class interval, so 2 students scored 0, 31 students scored 10, and so on. Calculate the mean of these results, and hence complete: “The mean Physics examination mark must be *at least* .....”
(2) Now suppose that all of the students scored the highest possible result in their class interval. Calculate the mean of these results, and hence complete: “The mean Physics examination mark must be *at most* .....”
(3) We now have two extreme values between which the actual mean must lie. Now suppose that all of the students scored the mid-interval value in their class interval. We assume that 2 students scored 4.5, 31 students scored 14.5, and so on.
- Calculate the mean of these results.
- How does this result compare with lower and upper limits found in 1 and 2?
- Copy and complete: “The mean Physics examination mark was approximately .....
(4) Discuss with your class how accurate you think an estimate of the mean using mid-interval values will be. How is this accuracy affected by the number and width of the class intervals?